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arXiv · 1110.2078

Quadratic $n$-ary Hom-Nambu algebras

Faouzi Ammar·Sami Mabrouk·Abdenacer Makhlouf
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Abstract

The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $α$-symmetric and $β$-invariant where $α$ and $β$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and that under suitable assumptions it reduces to a quadratic $(n-1)$-ary Hom-Nambu algebra.

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BibTeXRIS

Faouzi Ammar, Sami Mabrouk, Abdenacer Makhlouf. 2011-10-10. Quadratic $n$-ary Hom-Nambu algebras. https://arxiv.org/abs/1110.2078

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